Also there is already RollApp and there is already web-based LibreOffice - https://www.rollapp.com/search?query=... - there is actually a lot of different free and open-source apps available online. Unfortunately RollApp is payware - this means you can read files for free but not save. Cost is around 6 USD per month. RollApp can connect several cloud storages like Dropbox, Google Drive, Box, 4shared, OneDrive, Yandex Disk which is very good and appreciated. But still cannot connect with some also important cloud storages like ownCloud, MegaSync, SurDoc, ADrive - these storages are giving a lot of storage space - more than any others. Actually ownCloud gives as much as you are able to set up.

Another idea is to set up ability to save directly into cloud storage and make possible collaborative editing like it is in OneDrive - there you can use computer-based text editor (MS Word) and save directly to cloud storage and other partners can open the same file simultaneously and also edit at the same time. Then you can still use computer-based software, which has full functionality and still work collaboratively. This requires some cloud storage sync clients as extensions for LibreOffice but as far as I know, these do not exist. If there will be in future - it would be nice.

Yet another idea is to set up virtual machine in cloud and allow remote access to it. There are not much choices to access remotely regardless of network configuration. There is TeamViewer at http://www.teamviewer.com/ and if someone knows free and open-source replacement for TeamViewer - please let us know! This virtual machine could be set up as terminal server, e.g. using LTSP - http://www.ltsp.org/ - then everyone has its own session remotely. This means that you have to set up regular Linux installation with LTSP-packages installed and configured. Also that Linux installation is possible to connect organization's central authentication system like OpenLDAP or Microsoft software based system (using e.g. PGina http://pgina.org/ , SSSD https://fedorahosted.org/sssd/ , PowerBroker Open http://www.powerbrokeropen.org/ , Centrify http://www.centrify.com/ or whatever else).
Then there is possible to install several cloud storage sync clients and every user who logs in, can use these cloud storage sync clients. Then it all relies in top of regular operating system, which has full functionality to power up full version of LibreOffice and also all cloud storage sync clients.

As we all realize - using cloud-based software is great as long as you have connectivity. Therefore I would like to use also computer-based applications, which can save through cloud storage sync clients also to cloud. As we do not have direct extensions in LibreOffice to cloud storages then we can use ...(more)

Google's Chrome browser has an app called 'LibreOffice on rollApp' This runs within the browser as a server app as latest LibreOffice version and you can work with your files in Dropbox, Google Drive or similar clouds. I have tried the system on my Windows 8.1 and my HP Chromebox and it looks ok. As far as I know it is only free for the first month.

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Fernapp is nice but has some bugs and did not work with all functionalities. Tried FernApp 1.0.1 from here with 64-bit Ubuntu 14.04.2 LTS, 3.19.2 kernel and Icedtea Java 7u75 installed. Icedtea is default as Ubuntu offers it.

@Joe1234, although the executables are stored in the cloud, with a portable app, it then runs the code on your own computer. The software never "runs" in the cloud. With a web app, the software itself is running on remote computers, and just showing you the display through the web, so it is actually running there as well as being stored there.